Thousands of chemicals in wide commercial use and the environment have not been tested for adverse effects on humans. Accordingly, there is a need to improve chemical prioritization for in vivo toxicity testing and, ultimately, to find cell-based alternatives for evaluating the large inventory of potentially harmful compounds. Quantitative high throughput screening (qHTS) assays are multiple-concentration experiments with an important role in the efforts of the National Toxicology Program to meet these testing challenges and advance toxicology from a predominantly observational science to a predominantly predictive science. qHTS can simultaneously assay thousands of chemicals over a wide chemical space with reduced cost per substance. Previous approaches for making activity calls from qHTS data were based on pharmaceutical applications seeking to minimize false positives and usually relied on heuristics rather than statistical tests to make activity calls. We developed a three-stage algorithm to classify substances from qHTS data into statistically supported activity categories relevant to toxicological evaluation, seeking to improve sensitivity while minimizing Type I error rate (Shockley, 2012). The first stage of our approach fits a four-parameter Hill equation to find active substances with a robust concentration-response profile within the tested concentration range. The second stage finds relatively potent substances with substantial activity at the lowest tested concentration, substances not captured in the first stage. The third and final stage of the algorithm separates statistically significant profiles from responses that lack statistically compelling support, or inactives. This framework accommodates large volumes of qHTS data, tolerates missing data, and does not require replicate measurements. The three-stage algorithm described above is based on the Hill equation model. However, concentration-response data can be complex, and it may be more informative to find alternative patterns in the data not based on fits to sigmoidal curves. Parameter estimates derived from nonlinear regression model fits to data generated in qHTS experiments may accompany large uncertainties (Shockley, 2015). Therefore, we developed a weighted entropy score (WES) as a measure of average activity level to rank chemical in qHTS experiments (Shockley, 2014). WES scores can be used to rank all chemicals in a tested library without a pre-specified model structure, or WES can be used to complement existing approaches by ranking returned hits. WES outperforms rankings based on AC50 (estimated concentration of half-maximal response) across the full range of simulated conditions that are typical of qHTS studies. A nonparametric approach based on WES was used to estimate potency in qHTS profiles, where potency is estimated as the concentration producing the maximal rate of change in weighted entropy (Shockley, 2016). The new potency estimator (Point of Departure, PODWES) can accommodate any concentration-response pattern and does not depend on any pre-specified concentration-response model. In simulation studies based on the Hill equation model and the bell-shaped gain-loss model, PODWES estimates potency with greater precision and less bias compared to the conventional AC50 parameter. Also, PODWES produced more reproducible potency estimates than AC50 for a Tox21 Phase II estrogren receptor agonist in vitro data set. Tox21 qHTS experiments generate at least three (but possibly as many as 51) concentration-response profiles for each tested compound. The response patterns for a single compound may be similar or dissimilar with each other. We have developed an ANOVA-based method to flag compounds that have dissimilar response patterns that can be used for quality control of qHTS experiments at the level of the experiment or individual compounds. This approach can reliably cluster compounds into noise, homogeneous responses, or heterogeneous responses. Our novel method, called Cluster Analysis by Subgroups using ANOVA (CASANOVA), clusters compound-specific response patterns into statistically supported clusters that lead to trustworthy potency estimates (Shockley et al., 2019).